62.9.2 problem Ex 2

Internal problem ID [12833]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:26:01 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \frac {-y+x y^{\prime }}{\sqrt {x^{2}-y^{2}}}&=x y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 27

dsolve((x*diff(y(x),x)-y(x))/sqrt(x^2-y(x)^2)=x*diff(y(x),x),y(x), singsol=all)
 

\[ y-\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 29

DSolve[(x*D[y[x],x]-y[x])/Sqrt[x^2-y[x]^2]==x*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]